How do I get my concerns across with a stubborn DIL

Oh, baby mattresses!
My oldest DD had a cot mattress that was just like an ordinary bed mattress but with a waterproof cover.
Then it was de rigueur to have foam mattresses with holes at the head end. Cot bumpers were 'in' then 'out'. Tummy sleeping, side sleeping, back sleeping as the instructions from Health Visitors changed!
DC1 could climb out of the cot at an early age so I left the side down, with a stairgate in place.
Probably it's better that he can climb out of a low-level bed than tries to climb over the side of a cot and falls.

Fashions change but babies don't.

Somehow my DC

If she is worried about toxins in the mattress, why can't she put a cover over it that would separate the child from its innards. There must be a suitable "waterproof" available, wouldn't you think? Have mattresses changed drastically since her girls slept on them without harm? I can't fathom her concern.

I was lucky when I had my two children. Although our rented flat in an old converted house was cold and inclined to be damp, it was large and so were the rooms. The girls, born 5 years apart, stayed in a cot in our room until they started to climb out of it then, for safety, they got a bed in the hitherto spare bedroom. A floor bed there would definitely not have been a good idea as the only form of heating in the North facing room was a little coal fire. There wasn't even a power socket, let alone central heating. Personally, if such obvious hazards are absent, I can't see the danger in a floor based bed. Just keep the door shut (and get a baby alarm).

I say we were lucky - because I would have been unhappy putting such a young child in a separate nursery room, whether in a cot or a floor-bed. I do realise modern houses often have tiny rooms and offer no reasonable alternative.

I do hope the young lady isn't going to smother instead of mother her much wanted son. My Dad had difficulty keeping my Mum's maternal instincts under control when she eventually produced a son, 13 years after I came along and several years after she was told there could be no more children!

It's hard to believe cot mattresses are any more toxic than the single mattress that she's presumably going to use.
But I think you're overthinking this, if the bedroom's fully baby-proofed & they are vigilant, it doesn't sound particularly dangerous to me.

Whilst I respect your opinion, I beg to differ on it not being my business, especially since I’m being included on every step of this process. If I didn’t know, I’d not have anything to say, but since it’s being rammed down my throat, I’d say I have an opinion

If plugs are covered and it’s a clean floor I can’t see it’s a problem at 6 months boisterous babies can climb out of cots anyway I remember one of my grandaughters was always climbing out when she was really little ( mind you she was a great gymnast in her school years )

I'd advise your son that you don't want to know about the intricacies of raising baby and just sweet photos and nice news.

People get funny ideas about stuff, don't they?
I don't think there's anything you can do about this. Sleeping on the floor isn't too terrible, as long as anything that might harm your GS is removed.
But I do agree about the bottle. Does the GS really need a night feed at 6 months?

I’d be more concerned about the formula than the bed situation tbh. However, it’s none of your business really is it?